The influence maximization paradigm has been used by researchers in various fields in order to study how information spreads in social networks. While previously the attention was mostly on efficiency, more recently fairness issues have been taken into account in this scope. In the present paper, we propose to use randomization as a mean for achieving fairness. While this general idea is not new, it has not been applied in this area. Similar to previous works like Fish et al. (WWW ’19) and Tsang et al. (IJCAI ’19), we study the maximin criterion for (group) fairness. In contrast to their work however, we model the problem in such a way that, when choosing the seed sets, probabilistic strategies are possible rather than only deterministic ones. We introduce two different variants of this probabilistic problem, one that entails probabilistic strategies over nodes (node-based problem) and a second one that entails probabilistic strategies over sets of nodes (set-based problem). After analyzing the relation between the two probabilistic problems, we show that, while the original deterministic maximin problem was inapproximable, both probabilistic variants permit approximation algorithms that achieve a constant multiplicative factor of 1 − 1/e minus an additive arbitrarily small error that is due to the simulation of the information spread. For the node-based problem, the approximation is achieved by observing that a polynomial-sized linear program approximates the problem well. For the set-based problem, we show that a multiplicative-weight routine can yield the approximation result. For an experimental study, we provide implementations of multiplicative-weight routines for both the set-based and the node-based problems and compare the achieved fairness values to existing methods. Maybe non-surprisingly, we show that the ex-ante values, i.e., minimum expected value of an individual (or group) to obtain the information, of the computed probabilistic strategies are significantly larger than the (ex-post) fairness values of previous methods. This indicates that studying fairness via randomization is a worthwhile path to follow. Interestingly and maybe more surprisingly, we observe that even the ex-post fairness values, i.e., fairness values of sets sampled according to the probabilistic strategies computed by our routines, dominate over the fairness achieved by previous methods on many of the instances tested.

Learning directed acyclic graphs (DAGs) is long known a critical challenge at the core of probabilistic and causal modeling. The NoTears approach of (Zheng et al., 2018), through a differentiable function involving the matrix exponential trace $\mathrm{tr}(\exp(\cdot))$, opens up a way to learning DAGs via continuous optimization, though with a $O(d^3)$ complexity in the number $d$ of nodes. This paper presents a low-complexity model, called LoRAM for Low-Rank Additive Model, which combines low-rank matrix factorization with a sparsification mechanism for the continuous optimization of DAGs. The main contribution of the approach lies in an efficient gradient approximation method leveraging the low-rank property of the model, and its straightforward application to the computation of projections from graph matrices onto the DAG matrix space. The proposed method achieves a reduction from a cubic complexity to quadratic complexity while handling the same DAG characteristic function as NoTears, and scales easily up to thousands of nodes for the projection problem. The experiments show that the LoRAM achieves efficiency gains of orders of magnitude compared to the state-of-the-art at the expense of a very moderate accuracy loss in the considered range of sparse matrices, and with a low sensitivity to the rank choice of the model's low-rank component.

Traditionally, supervised machine learning algorithms are trained based on past data under the assumption that the past data is representative of the future. However, machine learning algorithms are increasingly being used in settings where the output of the algorithm changes the environment and hence, the data distribution. Indeed, online labor markets (Anagnostopoulos et al., 2018; Horton, 2010), predictive policing (Lum and Isaac, 2016), on-street parking (Dowling et al., 2020; Pierce and Shoup, 2018), and vehicle sharing markets (Banerjee et al., 2015) are all examples of real-world settings in which the algorithm's decisions change the underlying data distribution due to the fact that the algorithm interacts with strategic users. To address this problem, the machine learning community introduced the problem of performative prediction which models the data distribution as being decision-dependent thereby accounting for feedback induced distributional shift (Brown et al., 2020; Drusvyatskiy and Xiao, 2020; Mendler-Dünner et al., 2020; Miller et al., 2021; Perdomo et al., 2020). With the exception of (Brown et al., 2020), this work has focused on static environments. In many of the aforementioned application domains, however, the underlying data distribution also may have memory or even be changing dynamically in time. When a decision-making mechanism is announced it may take time to see the full effect of the decision as the environment and strategic data sources respond given their prior history or interactions. For example, many municipalities announce quarterly a new quasi-static set of prices for on-street parking. In this scenario, the institution may adjust parking rates for certain blocks in order to to achieve a desired occupancy range to reduce cruising phenomena and increase business district vitality (Dowling et al., 2017; Fiez et al., 2018; Pierce and Shoup, 2013; Shoup, 2006).

Practitioners often encounter challenging real-world problems that involve a simultaneous optimization of multiple objectives in a complex search space. To address these problems, we propose a practical multiobjective Bayesian optimization algorithm. It is an extension of the widely used Tree-structured Parzen Estimator (TPE) algorithm, called Multiobjective Tree-structured Parzen Estimator (MOTPE). We demonstrate that MOTPE approximates the Pareto fronts of a variety of benchmark problems and a convolutional neural network design problem better than existing methods through the numerical results. We also investigate how the configuration of MOTPE affects the behavior and the performance of the method and the effectiveness of asynchronous parallelization of the method based on the empirical results.

Mathematical optimization is the process of finding the best set of inputs that maximizes (or minimizes) the output of a function. In the field of optimization, the function being optimized is called the objective function. A wide range of out-of-the-box tools exist for solving optimization problems that only work with well-behaved functions, also called convex functions. Well-behaved functions contain a single optimum, whether it is a maximum or a minimum value. Here a function can be thought of as a surface with a single valley (minimum) and/or hill (maximum).

The COVID-19 pandemic has caused millions of cases and deaths and the AI-related scientific community, after being involved with detecting COVID-19 signs in medical images, has been now directing the efforts towards the development of methods that can predict the progression of the disease. This task is multimodal by its very nature and, recently, baseline results achieved on the publicly available AIforCOVID dataset have shown that chest X-ray scans and clinical information are useful to identify patients at risk of severe outcomes. While deep learning has shown superior performance in several medical fields, in most of the cases it considers unimodal data only. In this respect, when, which and how to fuse the different modalities is an open challenge in multimodal deep learning. To cope with these three questions here we present a novel approach optimizing the setup of a multimodal end-to-end model. It exploits Pareto multi-objective optimization working with a performance metric and the diversity score of multiple candidate unimodal neural networks to be fused. We test our method on the AIforCOVID dataset, attaining state-of-the-art results, not only outperforming the baseline performance but also being robust to external validation. Moreover, exploiting XAI algorithms we figure out a hierarchy among the modalities and we extract the features' intra-modality importance, enriching the trust on the predictions made by the model.

A computer-aided process planning system should ideally generate and optimize process plans to ensure the application of good manufacturing practices and maintain the consistency of the desired functional specifications of a part during its production processes. Crucial processes, such as selecting machining resources, determining set-up plans and sequencing operations of a part should be considered simultaneously to achieve global optimal solutions. In this paper, these processes are integrated and modelled as a constraint-based optimization problem, and a tabu search-based approach is proposed to solve it effectively. In the optimization model, costs of the utilized machines and cutting tools, machine changes, tool changes, set-ups and departure from good manufacturing practices (penalty function) are the optimization evaluation criteria. Precedence constraints from the geometric and manufacturing interactions between features and their related operations in a part are defined and classified according to their effects on the plan feasibility and processing quality.

This work presents the first projection-free algorithm to solve stochastic bi-level optimization problems, where the objective function depends on the solution of another stochastic optimization problem. The proposed $\textbf{S}$tochastic $\textbf{Bi}$-level $\textbf{F}$rank-$\textbf{W}$olfe ($\textbf{SBFW}$) algorithm can be applied to streaming settings and does not make use of large batches or checkpoints. The sample complexity of SBFW is shown to be $\mathcal{O}(\epsilon^{-3})$ for convex objectives and $\mathcal{O}(\epsilon^{-4})$ for non-convex objectives. Improved rates are derived for the stochastic compositional problem, which is a special case of the bi-level problem, and entails minimizing the composition of two expected-value functions. The proposed $\textbf{S}$tochastic $\textbf{C}$ompositional $\textbf{F}$rank-$\textbf{W}$olfe ($\textbf{SCFW}$) is shown to achieve a sample complexity of $\mathcal{O}(\epsilon^{-2})$ for convex objectives and $\mathcal{O}(\epsilon^{-3})$ for non-convex objectives, at par with the state-of-the-art sample complexities for projection-free algorithms solving single-level problems. We demonstrate the advantage of the proposed methods by solving the problem of matrix completion with denoising and the problem of policy value evaluation in reinforcement learning.

In order to define an optimization problem, you need three things: variables, constraints and an objective. The variables can take different values, the solver will try to find the best values for the variables. Constraints are things that are not allowed or boundaries, by setting these correctly you are sure that you will find a solution you can actually use in real life. The objective is the goal you have in the optimization problem, this is what you want to maximize or minimize. If it's not completely clear by now, here is a more thorough introduction.

My career as a practitioner and researcher in the data science space has spanned more than 30 years, and during that time I have seen a lot of new advanced analytics technologies – which were touted as "the latest and greatest," "cutting-edge," or "game-changing" or another similar superlative – sizzle and then fizzle. The hype cycles (as Gartner calls them) of these technologies were short – as they failed to deliver real-world business impact and attain long-term commercial viability. One advanced analytics technology that bucks that trend and has been around ever since I entered the professional arena in the early 1990s (and actually long before that with the introduction of linear programming in the 1940s) is mathematical optimization. For decades, mathematical optimization has been widely used by companies of all sizes and stripes to address their complex business problems. The secret to mathematical optimization's staying power is that it has consistently demonstrated that it is capable of generating optimal solutions to large-scale, real-world business problems – and has thereby produced significant business value.